Trajetórias hipotéticas de aprendizagem sobre funções exponenciais - Angiolin, Alexandra Garrote (2009)
This study has the objectives of investigating how to make constructivist perspectives of learning compatible with the planning the teaching-learning process, in the particular case of exponential functions and analyzing the performance of teachers of Mathematics with regard to the activities of the planning and development of teaching, in a way compatible with a constructivist perspective of learning. It is based on the work of Simon (1995) on hypothetical learning trajectories (HLTs). This is qualitative research involving two teachers of Mathematics from a state public school in Sao Paulo and their work with 77 students in the first year of Junior High School. We produced a hypothetical learning trajectory based on specific objectives and, taking as our reference hypotheses on student learning, we sought to propose tasks that involve the resolution of problems, investigation, the use of technologies, interdisciplinary approaches, applications to everyday situations and in other areas of knowledge. The HLT was implemented by the participating teachers in their own classes. From the analysis of the data obtained, we realized the complexity of producing proposals with the purpose of allowing students to build upon their own knowledge on the subject. In the same way, we experienced the challenge of facing teachers in developing tasks in this constructivist perspective, even when the intentions had been discussed and decided together. The teacher has a decisive role as, even when the teaching is planned within a constructivist perspective, what will really make this happen depends upon how he puts it into practice in the classroom. With regard to the students, when he is involved with less usual tasks that involve the reading of texts or the use of a computer, investigations show that these possibilities are promising in the sense of what occurs in learning, but various factors, which include the performance of the teacher himself, do not allow one to formulate more confident assertions upon these proposals